English
Related papers

Related papers: Note on a one-dimensional system of annihilating p…

200 papers

We consider systems of $N$ particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, we formally expect convergence towards the…

Analysis of PDEs · Mathematics 2013-09-11 Maxime Hauray

We study a $d$-dimensional branching Brownian motion (BBM) among Poissonian obstacles, where a random trap field in $\mathbb{R}^d$ is created via a Poisson point process. In the soft obstacle model, the trap field consists of a positive…

Probability · Mathematics 2023-07-18 Mehmet Öz

A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge - dependant upon only velocity - is assumed. The situation in which mobile negative ions balance the positive…

Analysis of PDEs · Mathematics 2010-01-06 Stephen Pankavich

The dynamics of a particle which is linearly coupled to a boson field is investigated. The boson field induces superselection rules for the momentum of the particle, if the field is infrared divergent. Thereby the Hamiltonian of the total…

Mathematical Physics · Physics 2009-11-07 Joachim Kupsch

The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…

Probability · Mathematics 2014-04-10 Yves Elskens , Etienne Pardoux

The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice-gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite…

Statistical Mechanics · Physics 2017-04-26 T. Imamura , K. Mallick , T. Sasamoto

For ASEP with step initial data and a second class particle started at the origin we prove that as time goes to infinity the second class particle almost surely achieves a velocity that is uniformly distributed on $[-1,1]$. This positively…

Probability · Mathematics 2022-04-13 Amol Aggarwal , Ivan Corwin , Promit Ghosal

We consider an interacting particle system on the one dimensional lattice $\bf Z$ modeling combustion. The process depends on two integer parameters $2\le a<M<\infty$. Particles move independently as continuous time simple symmetric random…

Probability · Mathematics 2016-09-07 Francis Comets , Jeremy Quastel , Alejandro F. Ramirez

Using Monte Carlo simulations we have studied the transition from an "active" steady state to an absorbing "inactive" state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the…

Statistical Mechanics · Physics 2009-10-31 Gyorgy Szabo , Maria Augusta Santos

We consider the motion of a Brownian particle in $\mathbb{R}$, moving between a particle fixed at the origin and another moving deterministically away at slow speed $\epsilon>0$. The middle particle interacts with its neighbours via a…

Probability · Mathematics 2008-07-04 Michael Allman , Volker Betz

From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the…

Probability · Mathematics 2021-03-12 Omer Angel , Gourab Ray , Yinon Spinka

In this paper we provide an extension of the model discussed in [arXiv:1504.08283] describing two singularly interacting particles on the half-line. In this model, the particles are interacting only whenever at least one particle is…

Mathematical Physics · Physics 2018-01-04 Joachim Kerner , Tobias Mühlenbruch

We study the Fleming--Viot particle system in a discrete state space, in the regime of a fast selection mechanism, namely with killing rates which grow to infinity. This asymptotics creates a time scale separation which results in the…

Probability · Mathematics 2024-07-03 Lucas Journel , Tony Lelièvre , Julien Reygner

We analyze the annihilation of equally-charged particles based on the Brownian motion model built by F. Dyson for $N$ particles with charge $q$ interacting via the log-Coulomb potential on the unitary circle at a reduced inverse temperature…

Statistical Mechanics · Physics 2020-01-15 Cristhian Gonzalez-Ortiz , Gabriel Tellez

We consider the Kawasaki dynamics of two types of particles under a killing effect on a $d$-dimensional square lattice. Particles move with possibly different jump rates depending on their types. The killing effect acts when particles of…

Probability · Mathematics 2019-03-25 Anna De Masi , Tadahisa Funaki , Errico Presutti , Maria Eulalia Vares

We show explicitly that there is particle creation in a static spacetime. This is done by studying the field in a coordinate system based on a physical principle which has recently been proposed. There the field is quantized by decomposing…

High Energy Physics - Theory · Physics 2015-06-26 D. J. Lamb , A. Z. Capri , S. M. Roy

We consider a body in a parallel flow of non-interacting particles. One can imagine that the flow is highly rarefied or consists of light rays. The interaction of particles with the body is perfectly elastic. We introduce the notions of a…

Optics · Physics 2009-01-20 Alena Aleksenko , Alexander Plakhov

Consider the random set composed of particles initially distributed on Zd, d >= 2, according to a Poisson point process of intensity u > 0 and moving as independent simple symmetric random walks, the trap particles. We are interested in the…

Probability · Mathematics 2025-07-22 Gonzalo Panizo , Carlos Martínez

Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. A triple…

Probability · Mathematics 2015-01-30 Andrey Sarantsev

In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…

Probability · Mathematics 2015-05-29 Anja Sturm , Jan M. Swart